Reaction Rates

Core Concept

Chemical kinetics asks a different question than thermodynamics. Thermodynamics tells you whether a reaction can happen; kinetics tells you how fast it happens. The reaction rate is a measure of how quickly reactants are consumed (or products are formed), reported as a change in concentration (molarity, M) per unit time. For a reaction like A → B, the rate is defined so that it is always a positive number: reactants get a negative sign because their concentration decreases, and products get a positive sign.

Key Ideas

• Rate is an extensive property of concentration change. We track concentration (M), not mass or moles, so that rate can be compared across different reaction vessels.
• Average rate vs. instantaneous rate. Average rate covers a finite time interval; instantaneous rate is the slope of the concentration–time curve at a single instant.
• Stoichiometry links the rates. In 2 NO₂ → 2 NO + O₂, NO is produced twice as fast as O₂ is produced, and NO₂ disappears at the same rate NO appears.
• Rates change over time. As reactants are used up, most reactions slow down, so the rate is highest at the start (t = 0).

Equations and Variables

For a general reaction aA + bB → cC + dD, the rate is expressed so that every species gives the same numerical value:

Rate = -1aΔ[A]Δt = -1bΔ[B]Δt = +1cΔ[C]Δt = +1dΔ[D]Δt

• [A], [B], [C], [D] = molar concentrations (M = mol/L)
• Δt = change in time (s)
• Δ[X] = [X]final − [X]initial (M)
• a, b, c, d = stoichiometric coefficients (unitless)

For a simple one-to-one reaction A → B, this collapses to:

Rate = -Δ[A]Δt = +Δ[B]Δt

Units of rate are always concentration per time, most commonly M·s⁻¹.

How It Works

Imagine a reaction vessel where reactant A is slowly turning into product B. If [A] falls from 1.00 M to 0.80 M over 10.0 seconds, then Δ[A] = 0.80 − 1.00 = −0.20 M. The rate of consumption of A is −Δ[A]/Δt = −(−0.20 M)/10.0 s = 0.020 M/s. Because the sign convention already accounts for the decrease, the reported rate is positive.

The stoichiometric factors (1/a, 1/b, …) exist so that the rate means the same thing no matter which chemical you watch. Consider 2 H₂O₂ → 2 H₂O + O₂. Every time O₂ forms at 0.0050 M/s, H₂O₂ disappears at twice that rate (0.010 M/s) because two molecules of peroxide are consumed for every one O₂ produced. Dividing each by its coefficient makes them equal:

Rate = -12Δ[H₂O₂]Δt = Δ[O₂]Δt

The instantaneous rate is found by drawing a tangent line to the concentration–time curve at the time of interest and taking its slope. At t = 0 this is the initial rate, a quantity we use heavily later because concentrations are known exactly at the start.

Worked Example

The reaction 2 N₂O₅(g) → 4 NO₂(g) + O₂(g) is monitored. Over a 100-second interval, [N₂O₅] decreases from 0.0500 M to 0.0400 M.

(a) Average rate of N₂O₅ consumption.

Rate = -Δ[N₂O₅]Δt = -0.0400 - 0.0500 M100 s = --0.0100 M100 s = 1.00 × 10^-4 M s^-1

(b) Rate of O₂ formation over the same interval.

One O₂ is produced for every two N₂O₅ consumed, so O₂ forms at half the rate:

Δ[O₂]Δt = 12(1.00 × 10^-4 M s^-1) = 5.0 × 10^-5 M s^-1

(c) Rate of NO₂ formation.

Four NO₂ form per two N₂O₅ consumed, a 2:1 ratio, so NO₂ forms twice as fast as N₂O₅ disappears:

Δ[NO₂]Δt = 2(1.00 × 10^-4 M s^-1) = 2.0 × 10^-4 M s^-1

Notice that all three answers are positive, and the fastest-changing species (NO₂) has the largest coefficient.

How it works

Imagine a reaction vessel where reactant A is slowly turning into product B. If [A] falls from 1.00 M to 0.80 M over 10.0 seconds, then Δ[A] = 0.80 − 1.00 = −0.20 M. The rate of consumption of A is −Δ[A]/Δt = −(−0.20 M)/10.0 s = 0.020 M/s. Because the sign convention already accounts for the decrease, the reported rate is positive.

The stoichiometric factors (1/a, 1/b, …) exist so that the rate means the same thing no matter which chemical you watch. Consider 2 H₂O₂ → 2 H₂O + O₂. Every time O₂ forms at 0.0050 M/s, H₂O₂ disappears at twice that rate (0.010 M/s) because two molecules of peroxide are consumed for every one O₂ produced. Dividing each by its coefficient makes them equal:

Rate = -12Δ[H₂O₂]Δt = Δ[O₂]Δt

The instantaneous rate is found by drawing a tangent line to the concentration–time curve at the time of interest and taking its slope. At t = 0 this is the initial rate, a quantity we use heavily later because concentrations are known exactly at the start.

Common confusions

• "Rate is negative for reactants." The concentration change Δ[A] is negative, but the rate itself is defined with a minus sign so it stays positive. Do not report a negative rate.
• Forgetting stoichiometric coefficients. The rate of NO₂ formation is twice the rate of O₂ formation in the N₂O₅ example. Coefficients matter.
• Confusing average and instantaneous rate. Average rate is over a window; instantaneous is a tangent slope. They agree only when the rate is constant.
• Using moles instead of molarity. Rate uses concentration so it is independent of vessel size.

Quick review

1. Define the rate of a reaction in words and with a formula.
2. Why is there a negative sign on reactant terms?
3. In 2 H₂ + O₂ → 2 H₂O, how does the rate of H₂ consumption compare with the rate of H₂O formation?
4. Name four factors that influence reaction rate.
5. Why is the initial rate preferred in many experiments?